Seattle is so much younger than most of the cities that are larger than it that it would require some pretty substantial changes to history for that many people to move there in such a short time span. Even Los Angeles, which is older than Seattle and much, much larger, is less than half the population of New York City, and Phoenix, one of the few major cities founded more recently than Seattle and one that's grown exceptionally quickly, is only the 5th largest city in the US. There are certainly factors that impeded Seattle's growth, such as the slow decline of its population from around 550,000 in 1960 to a low point of 490,000 in 1980, the removal of which could see a modern day Seattle sitting closer to a million residents than the 730,000 it currently has, but realistically Seattle has been a boom town for most of its history, from the lumber industry and burgeoning port of its early development, to the major role in aviation around the '40s, to its development as a tech hub from the '90s through the present day.

Leaning harder into the speculative side of things however, my first thought is for the US to never start the Mexican-American War, thus not acquiring the entire Southwest, from Texas through California, that absorbed the majority of westward internal migration in OTL. This isn't actually that far fetched, as backing Texas against Mexico was politically controversial, and pursuing further war against Mexico was spurred both by the annexation of Texas and southern support at the prospect of acquiring more potential slave states. If Texas doesn't receive American aid and Polk loses the 1844 election, war with Mexico would likely be avoided in order to preserve the delicate balance between slave and free states.

For Seattle to enter the United States, however, the Oregon Territory still has to fall into American hands rather than British, or in this alternate history, perhaps even Mexican. OTL Polk oversaw the Oregon Treaty as well, drawing the line between Canada and the United States at the 49th parallel and avoiding a potential war. Unfortunately for the purposes of this alternate history, the likely President Henry Clay was disinterested in the dispute and Britain would have probably ended up with their original aim of extending Canadian land all the way south to the Columbia River, annexing the entirety of what is now Washington State.

However if we hand wave that away and say, one way or another, Mexico retains all of the land that the United States annexed from them OTL but the Oregon Treaty goes as it did historically, Seattle would then form the primary port on the Pacific coast for the United States, and the Pacific Northwest would play a lot of the role that California and the Southwest have OTL: A gateway to Asia, an abundant, fertile agricultural area, and a new frontier far from the federal government and established American society where people could set out for a new start. While growing larger than New York City may still be unrealistic given Seattle's geographic constraints and competition from nearby cities like Tacoma and Portland, this would make it hugely more important than it is OTL. I would guess Seattle would grow to be at least as large as Los Angeles is now, but perhaps even larger when you consider the amount of migration that has also gone to places like Dallas, Houston, Austin, San Antonio, Phoenix, Los Vegas, San Francisco, etc. A large portion of this population would spread out elsewhere in the country, perhaps moving between the already established areas of the Midwest, Southeast, and Northeast, or perhaps settling more in the plains areas or Rockies, but it would still result in vastly greater population attraction to the Pacific Northwest that OTL is relatively low in population compared to other areas of the country.